Thanks to all for your suggestions.
@JJacquelin: your derivation is very helpful.
The remaining equation without the boundary conditions:
(F'(x)-1)(F(x)+k)=C
should be also solvable for more complex situations. Mathematica delivers a general solution in terms of the Lambert W (product...
Hi all,
I'm trying to find an analytical solution to the following integro-differential equation:
a f'(x)\int_0^x f(x)dx + b f'(x) + a [f(x)]^2 - a f(x) = 0
with initial condition:
f(0)=1
This is a simplified problem for which I know the solution: f(x)=1.
I'm trying to find...